Oh that's a bummer. Should be in your ownership documents somewhere. I think the rule is often that you own the fence "on the right". But I don't think that's a hard and fast rule.
Yeah, I don't think it is. It's awkward because it's not the fence on the left or right, it's the one facing the house at the end of the garden... but as the neighbour's house is side-on to mine, it's actually their left fence.
I just found my transfer deed and it says that any fences or walls not marked with a T on the Plan (which none of them are) are 'party fences and walls' and shall be 'repairable and maintained as such'.
I looked up 'party fences' and found this in an article about party fence walls and fences:
An ordinary garden fence is not covered under the Party Wall Act.
Normal fences made of timber or concrete posts and timber panels do not come under the 1996 Act. Your deeds may state that the fence to your property is a 'party fence' but this has a different meaning and is unconnected with the 1996 Act. Usually this means that the fences are maintainable by both owners and it follows that the fences are also erected on the boundary. So, that reads to me as if we're both responsible for repair and maintenance of the fence, but I can't do anything from my side because I can't get at the fence without cutting down all the trees and bushes.